Information on Result #1051407
Linear OOA(2127, 524293, F2, 4, 12) (dual of [(524293, 4), 2097045, 13]-NRT-code), using OOA 4-folding based on linear OA(2127, 2097172, F2, 12) (dual of [2097172, 2097045, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(2127, 2097174, F2, 12) (dual of [2097174, 2097047, 13]-code), using
- 1 times truncation [i] based on linear OA(2128, 2097175, F2, 13) (dual of [2097175, 2097047, 14]-code), using
- construction X4 applied to Ce(12) ⊂ Ce(10) [i] based on
- linear OA(2127, 2097152, F2, 13) (dual of [2097152, 2097025, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(2106, 2097152, F2, 11) (dual of [2097152, 2097046, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(222, 23, F2, 21) (dual of [23, 1, 22]-code), using
- strength reduction [i] based on linear OA(222, 23, F2, 22) (dual of [23, 1, 23]-code or 23-arc in PG(21,2)), using
- dual of repetition code with length 23 [i]
- strength reduction [i] based on linear OA(222, 23, F2, 22) (dual of [23, 1, 23]-code or 23-arc in PG(21,2)), using
- linear OA(21, 23, F2, 1) (dual of [23, 22, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to Ce(12) ⊂ Ce(10) [i] based on
- 1 times truncation [i] based on linear OA(2128, 2097175, F2, 13) (dual of [2097175, 2097047, 14]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(2127, 524293, F2, 5, 12) (dual of [(524293, 5), 2621338, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2127, 524293, F2, 6, 12) (dual of [(524293, 6), 3145631, 13]-NRT-code) | [i] | ||
| 3 | Linear OOA(2127, 524293, F2, 7, 12) (dual of [(524293, 7), 3669924, 13]-NRT-code) | [i] | ||
| 4 | Linear OOA(2127, 524293, F2, 8, 12) (dual of [(524293, 8), 4194217, 13]-NRT-code) | [i] | ||
| 5 | Digital (115, 127, 524293)-net over F2 | [i] | ||